Controlling cosine-Gaussian beams in linear media with quadratic external potential

Abstract

We investigate both analytically and numerically the propagation dynamic of on-axis and off-axis cosine-Gaussian (CG) beams in a linear medium with quadratic external potential. CG beam propagation evolves periodically with a period depended on the potential depth (α) and whether the beam shape is symmetrical with respect to optical axis. In each period, the CG beam first splits into two sub-beams with different accelerated direction; they then reverse the accelerated direction owing to the quadratic external potential and finally merge again to reproduce its initial shape, and the whole process repeats periodically. The intensity oscillation period of the off-axis CG beam is double times than that of the on-axis one. At the special position, the beam (or spectral) shape is strongly related to the initial spectral (beam) shape. The corresponding scaled relationship is that the spatial intensity I x (or spatial frequency axis k) is α times the spectral intensity I k (or space axis x). The interaction of two spatially separated CG beams still exhibit periodic evolution with complex structure in the regime of focal point. The propagation dynamics of two-dimensional CG beams are also presented. When the propagation distance is exactly an integer multiple of half period, there are four focal points in the diagonal position.

A conceptual review on Bessel beams

“…In addition to 1D Cosine beams, we can also generate 2D Cosine beams whose propagation is two-dimensionally non-diffracted. However, these beams have completely different features with respect to BBs [58][59][60]. While 2D BB have circular rings with central bright spot, 2D Cosine beam have an array of square-type optical needles.…”

Cosine-Gaussian breathers controlled by the initial conditions in highly nonlocal media

“…The amplitude of CG breathers at the waist plane is expressed as [27] Ψ(x w , y w ) = C 0 cos ax w w x0 cos by w w y0 exp…”

An intriguing interpretation of Cosine beams

“…It is possible to understand the real Cosine beams through the truncation of Cosine beams. Depending on the interfering beams, we can apodize the Cosine beam, and we can create various types of Cosine beams like Cosine-Gauss / Cos-Gauss (CG) beam [19], Cosine-Hermite-Gauss (CHG) beam [11], Super-Gaussian-Cosine (SGC) beam [7], etc. As shown in Fig.…”

“…The self-healing and nondiffraction nature [11,16] of Cosine beams make them utilized in fundamental and applied optics. To name a few, various kinds of Cosine beams with and without apodization are used in light-sheet microscopy [17], in the interaction with uniaxial crystal [18], in the interaction of linear and nonlinear media [19,20], in periodic potential optical lattices [21], in the study of spherical particles [22], in optical wireless communication [23], and in plasmonics [24].…”